Right Triangle Identification: Analyzing a Given Triangle Drawing

Q: How can I tell if a triangle is a right triangle just by looking?

Look for perpendicular lines (horizontal meeting vertical), a square corner symbol, or sides that form an obvious $ 90^\circ $ angle. The small square in the corner is the universal symbol for a right angle!

Q: What if the triangle doesn't look perfectly square at the corner?

Use the Pythagorean theorem! If $ a^2 + b^2 = c^2 $ where c is the longest side, then it's a right triangle. Don't rely only on visual appearance.

Q: Can a triangle have more than one right angle?

No! A triangle's angles must add up to $ 180^\circ $. If it had two $ 90^\circ $ angles, that would already be $ 180^\circ $ with no room for a third angle.

Q: What's special about the sides in a right triangle?

The two sides forming the right angle are called legs, and the longest side (opposite the right angle) is the hypotenuse. The hypotenuse is always the longest side!

Q: Why does perpendicular mean 90 degrees?

Perpendicular means "at right angles to." When two lines meet perpendicularly, they form four equal $ 90^\circ $ angles. This is the definition of perpendicular!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine whether the triangle is right-angled

00:03 The triangle has a right angle (90°) therefore it is a right-angled triangle

00:06 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Is the triangle in the drawing a right triangle?

2

Step-by-step solution

To determine if the given triangle is a right triangle, we will analyze its drawing:

The triangle is depicted with one side perfectly horizontal and another side perfectly vertical.
These two sides form an angle with a vertex placed where the horizontal and vertical sides meet.
The angle formed at this point must be $90^\circ$ since the horizontal and vertical lines are by definition perpendicular to each other.
When a triangle has one angle equal to $90^\circ$ , it confirms that the triangle is a right triangle.

Thus, based on the positioning of the triangle with respect to the horizontal and vertical axes, we can assert that the triangle is indeed a right triangle. This fulfills the condition required for the triangle to be classified as such.

Therefore, the solution to the problem is: Yes.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Definition: Right triangle has exactly one $90^\circ$ angle
Technique: Look for perpendicular lines forming square corner symbol
Check: Horizontal meets vertical at $90^\circ$ creates right angle ✓

Common Mistakes

Avoid these frequent errors

Assuming all triangles with square corners are right triangles
Don't trust drawings without checking measurements = wrong conclusions! Visual representations can be misleading or not drawn to scale. Always verify using angle measurements, Pythagorean theorem, or given perpendicular indicators.

Practice Quiz

Test your knowledge with interactive questions

In a right triangle, the side opposite the right angle is called....?

FAQ

Everything you need to know about this question

How can I tell if a triangle is a right triangle just by looking?

+

Look for perpendicular lines (horizontal meeting vertical), a square corner symbol, or sides that form an obvious $90^\circ$ angle. The small square in the corner is the universal symbol for a right angle!

What if the triangle doesn't look perfectly square at the corner?

+

Use the Pythagorean theorem! If $a^2 + b^2 = c^2$ where c is the longest side, then it's a right triangle. Don't rely only on visual appearance.

Can a triangle have more than one right angle?

+

No! A triangle's angles must add up to $180^\circ$ . If it had two $90^\circ$ angles, that would already be $180^\circ$ with no room for a third angle.

What's special about the sides in a right triangle?

+

The two sides forming the right angle are called legs, and the longest side (opposite the right angle) is the hypotenuse. The hypotenuse is always the longest side!

Why does perpendicular mean 90 degrees?

+

Perpendicular means "at right angles to." When two lines meet perpendicularly, they form four equal $90^\circ$ angles. This is the definition of perpendicular!

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Right Triangle Identification: Analyzing a Given Triangle Drawing

Right Angle Recognition with Visual Elements

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